SIMONS COMPUTATIONAL THEORIES OF THE BRAIN APRIL 18, 2018 DECODING THE FUNCTIONAL NETWORKS OF CEREBRAL CORTEX

SIMONS COMPUTATIONAL THEORIES OF THE BRAIN APRIL 18, 2018 DECODING THE FUNCTIONAL NETWORKS OF CEREBRAL CORTEX

VISUAL CORTEX DISPLAYS ACTIVITY NOT DIRECTLY TIED TO VISUAL STIMULI J. Physiol. (I959) I47, 226-238 SINGLE UNIT ACTIVITY IN STRIATE CORTEX OF UNRESTRAINED CATS BY D. H. HUBEL* From the Department of Neurophysiology, Walter Reed Army Institute of Research, Walter Reed Army Medical Center, Washington 12, D.C., U.S.A. (Received 15 December 1958) Background activity In the unrestrained preparation most units showed activity in the absence of intentional stimulation on the part of the observer. As the cat looked about, spurts and pauses in firing were seen to accompany eye movements. When the eyes were closed either passively by the observer or by the cat, firing usually persisted, although it was generally less active. Even when the room was made completely dark most units continued to fire.

GOALS Extend theories of cortical computation from the average case to single trials using network based analytical tools Incorporate a more comprehensive sampling of the network to include unbiased sample of neurons

OUTLINE Mouse V1 & high speed two-photon imaging What are functional networks? Functional networks accurately predict neuronal activity Higher order structure in functional networks Assemblies

OUR EXPERIMENTAL SET-UP Awake behaving (ambulating) animals Window over V1 Head bar Top down view

RETINOTOPY TO CONFIRM VISUAL CORTEX Window over V1 Head bar Top down view Intrinsic Imaging Two Photon Imaging

IN VIVO 2P SOMATIC IMAGING OF VISUALLY EVOKED ACTIVITY

CORTICAL V1 MICROCIRCUIT DYNAMICS IMAGED WITH HOPS

MULTINEURONAL RESPONSES TO DRIFTING GRATINGS grating direction neurons 50 100 150 R normalized activity (A.U.) 10 cm/s Running speed 50 100 150 200 250 (s)

REPRESENTATIVE TUNED AND UNTUNED RESPONSES grating direction Cell 1 Cell 2 Cell 3 Cell 4 Cell 5

TUNED NEURONS SHOW VARIABLE SINGLE TRIAL ACTIVITY 90 trials 180 0 270 norm. fluorescence time

TUNED NEURONS SHOW VARIABLE SINGLE TRIAL ACTIVITY 1 trials 90 180 0 270 norm. fluorescence trials time 30 1 s

TUNING DOESN T PREDICT SINGLE TRIAL RESPONSES VERY WELL probability density 20 15 10 5 tuned (2613 / 4535) untuned (1922 / 4535) 0 0 0.2 0.4 0.6 0.8 1 variance explained

OUTLINE Mouse V1 & high speed two-photon imaging What are functional networks? Functional networks accurately predict neuronal activity Higher order structure in functional networks

Network: A mathema)cal representa)on of a real-world complex system defined by a collec)on of nodes (ver)ces) and links (edges) between pairs of nodes.

BUILDING A FUNCTIONAL NETWORK USING PAIRWISE PARTIAL CORRELATION Edge weight = partial correlation w = 0.51 50% 20 sec within movie activity i,j remaining movie average i,j within movie average k i,j Directionality = correlogram lag zero lag i j t max

FUNCTIONAL NETWORKS CONTAIN EDGES BETWEEN TUNED AND UNTUNED NEURONS tuned neuron id untuned 0.4 neuron id tuned untuned 0.2 0 edge weight

FUNCTIONAL NETWORKS REFLECT TUNING IN THE POPULATION neuron id neuron id tuned untuned tuned untuned 0.4 0.2 0 edge weight edge weight 0.1 0.08 0.06 tuned - tuned tuned - untuned untuned - untuned 0.04 0 90 180 difference in preferred direction (o)

OUTLINE Mouse V1 & high speed two-photon imaging What are functional networks? Functional networks accurately predict neuronal activity Higher order structure in functional networks

MODELING NEURON RESPONSES USING FUNCTIONAL NETWORKS W 1 W2 50% ΔF 20 sec rescale W n input neuron activity weights tuned neuron id untuned 0.4 neuron id tuned untuned 0.2 0 edge weight

ACCURATE PREDICTION OF MOMENT TO MOMENT ACTIVITY USING FUNCTIONAL NETWORKS W1 50% ΔF 20 sec 50% ΔF 20 sec W 2 Wn rescale input neuron activity weights predicted activity / measured activity

FUNCTIONAL NETWORKS PROVIDE NEAR OPTIMAL PREDICTIONS OF SINGLE TRIAL RESPONSES 50% predicted activity / measured activity 20 sec optimal weights (MSE) 10-1 10-2 10-3 10-2 10-1 graph weights (MSE)

FUNCTIONAL NETWORKS ALSO PREDICT TUNING 600 Cosine similarity < 1 90 120 60 150 120 Cosine similarity = 1 90 60 30 neuron count 400 180 150 210 240 270 300 30 330 0 180 210 240 270 300 330 0 200 0 0 0.2 0.4 0.6 0.8 1 predicted tuning vector (cosine similarity)

POPULATION SIZE UNDERLIES PREDICTION ACCURACY population variance explained 0.9 0.8 0.7 0.6 0.5 0.4 50 100 150 200 250 300 350 neurons

LARGE WEIGHTS CONTRIBUTE DISPROPORTIONATELY TO PREDICTION ACCURACY 1 0.9 strongest first random weakest first % total MSE 0.8 0.7 0.6 0.5 0.4 0 0.2 0.4 0.6 0.8 fraction weight removed

RECURRENT CONNECTIONS ARE BIASED TOWARD LARGE EDGE WEIGHTS reciprocal probability (fold over random) 10 1 within tuned within untuned between tuned & untuned 0 0.2 0.4 0.6 0.8 edge weight threshold (quantile)

OUTLINE Mouse V1 & high speed two-photon imaging What are functional networks? Functional networks accurately predict neuronal activity moment to moment prediction Higher order structure in functional networks

BEYOND PAIRWISE undirected Directed fan-in fan-out middleman cycle

TRIPLET MOTIF STRUCTURE IN FUNCTIONAL NETWORKS undirected cycle middle-man fan-in fan-out 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 clustering coefficient (fold over Random)

variance explained TRIPLET MOTIF STRUCTURE UNDERLIES PREDICTION ACCURACY 1 undirected cycle 0.8 middle fan-in 0.6 fan-out 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 clustering coefficient (fold over ER) 0.4 middle 0.2-0.5 Dominance of Motif 0 0.5 1 (z-score)

CONCLUSIONS Neurons are variable making prediction of single trial activity from tuning properties difficult Functional networks provide near optimal predictions of activity in individual neurons And predict tuning Triplet correlations are predictive of more than 90% of a moment to moment activity

ASSEMBLIES Data demonstrates a loose coalition of neurons that covary with one another and consequently are predictive of one another Multineuronal activity shows pairwise timing differences as indicated by the fact that the majority of entries in the matrix are asymmetric But many unknowns

ACKNOWLEDGMENTS Current Lab Joe Dechery Vaughn Spurrier Maayan Levy Peter Malonis Zania Zayyad Kyle Bojanek Subhodh Kotekal Isabel Garon Carolina Yu Harrison Grier Friederice Pirschen Anne Havlik Lab Alumni Brendan Chambers Alex Sadovsky Peter Kruskal Melissa Runfeldt Lucy Li SJ Weinberg Veronika Hanko Lane McIntosh Suchin Gururangan Charles Frye Alexa Carlson Caroline Heimerl Isabella Penido Areknaz Khaligian Audrey Sederberg FACCTS